The issue is some underlying error in Ubuntu Gutsy with package management… and the solution is to install Flash Player 9 directly via the Adobe website.
Installing Without Command Line
Yes, you can install this without troubling yourself to open the command line at all. (Command line instructions are below).
Right-click on the downloaded installation file and choose “Extract Here” from the menu.
Now open up the new folder and double-click on flashplayer-installer. When prompted, choose to “Run in Terminal”
You’ll have to click inside the window and hit the Enter key and then the y key at the prompts. (Make sure you have Firefox closed)
Now your Flash player should be working just fine.
Installing from the Command Line
If you prefer to install from the command line, you can run the following commands to download and install flash player. Make sure you’ve closed all instances of Firefox before you start this.
Verifying Installation
tar xvfz install_flash_player_9_linux
cd install_flash_player_9_linux
./flashplayer-installer
Type about:plugins into the address bar, and verify that you see Shockwave Flash in the list.
That should be all you need to do.
Download Flash Player 9 for Linux